Most rosette comps require a very high skill set. I looked at what you have and don't see any that are high enough to be able to see comps with rosettes.

If there is a special horse you are using a link would help.

What would u need skill wise?

As an example, I have the top Trot competition on the server -

L.C.E.C Trot
Trot race

Information
Equestrian Centre: Lake Cootapatamba E.C
Difficulty: 96.00%
Level required: from 9,216 to 18,432 in trot
Frequency: Once every 3 hours
Prestige:
84.6068
84.61%
Reserved for horses with more than 20 wins

so the minimum skill requirement is 9216 in trot to enter, which means that only the elite horses can enter to keep m,y prestige up.

If you click on Rankings - Equestrian Centres and the 'Best competitions, you can click on each named competition and see the minimum requirement to enter and if they have a rosette.